Abstract
We build a simple dissipative analytical model considering an averaged restricted 3-body problem taking into account the effect of the oblateness of a planet on a small satellite and on its perturber. We apply this model to the inner Uranian system and we follow the dynamical evolution of the satellites Cressida or Desdemona, these latter being close to a 3:1 commensurability with the large satellite Miranda. Our analysis shows that the positions of the two inner satellites, on both sides of the exact resonance, are temporary, Cressida having already crossed the resonance, and Desdemona approaching the commensurability to jump over later on.
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